Depending on the airport, sometimes the airport website will list all the non-stop destinations served as an advertising tool. (
http://www.airports.com/) I looked at the website for Logan, but did not see a comprehensive list. However if you look at the "Departures" under the "Quick Jump" dropdown it does list all scheduled departures for that day. Not too helpful for destinations served less than daily, but a start.
http://www.massport.com/logan/default.aspx